Oscillatory behavior in discrete slow power-law models

Discrete mathematical slow oscillatory models are proposed to describe biological interactions between two populations by considering power-law functions. Conditions for slow convergence to the equilibrium point are imposed on model parameters. Moreover, to obtain oscillatory solutions we prove that...

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Bibliographic Details
Published inNonlinear dynamics Vol. 102; no. 3; pp. 1553 - 1566
Main Authors Jerez, Silvia, Pliego, Emilene, Solis, Francisco J.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.11.2020
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Mathematical models
Mechanical Engineering
Original Paper
Parameters
Power law
Two dimensional models
Vibration
Lotka–Volterra systems
65Z05
92D25
Discrete power-law models
37N25
Slow systems
Schwarzian derivative
Bone remodeling
Oscillatory behavior
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Summary:Discrete mathematical slow oscillatory models are proposed to describe biological interactions between two populations by considering power-law functions. Conditions for slow convergence to the equilibrium point are imposed on model parameters. Moreover, to obtain oscillatory solutions we prove that model exponents may be parameterized by only one parameter. As a by-product, we also discover a family of functions that can be regarded as a two-dimensional generalization of the Schwarzian derivative. Diverse particular model cases are analyzed numerically in order to show orbital solutions. Finally, applications for biochemical and population models are presented.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05982-z